Plot the vector in a Cartesian graph based on the coordinates of some
ambient chart.

The vector is drawn in terms of two (2D graphics) or three (3D graphics)
coordinates of a given chart, called hereafter the ambient chart.
The vector’s base point \(p\) (or its image \(\Phi(p)\) by some
differentiable mapping \(\Phi\)) must lie in the ambient chart’s domain.
If \(\Phi\) is different from the identity mapping, the vector
actually depicted is \(\mathrm{d}\Phi_p(v)\), where \(v\) is the current
vector (self) (see the example of a vector tangent to the
2-sphere below, where \(\Phi: S^2 \to \RR^3\)).

INPUT:

chart – (default: None) the ambient chart (see above); if
None, it is set to the default chart of the open set containing
the point at which the vector (or the vector image via the
differential \(\mathrm{d}\Phi_p\) of mapping) is defined

ambient_coords – (default: None) tuple containing the 2
or 3 coordinates of the ambient chart in terms of which the plot
is performed; if None, all the coordinates of the ambient
chart are considered

mapping – (default: None)
DiffMap;
differentiable mapping \(\Phi\) providing the link between the
point \(p\) at which the vector is defined and the ambient chart
chart: the domain of chart must contain \(\Phi(p)\);
if None, the identity mapping is assumed

scale – (default: 1) value by which the length of the arrow
representing the vector is multiplied

color – (default: ‘blue’) color of the arrow representing the
vector

print_label – (boolean; default: True) determines whether a
label is printed next to the arrow representing the vector

label – (string; default: None) label printed next to the
arrow representing the vector; if None, the vector’s symbol is
used, if any

label_color – (default: None) color to print the label;
if None, the value of color is used

fontsize – (default: 10) size of the font used to print the
label

label_offset – (default: 0.1) determines the separation between
the vector arrow and the label

parameters – (default: None) dictionary giving the numerical
values of the parameters that may appear in the coordinate expression
of self (see example below)

**extra_options – extra options for the arrow plot, like
linestyle, width or arrowsize (see
arrow2d() and
arrow3d() for details)

OUTPUT:

a graphic object, either an instance of
Graphics for a 2D plot (i.e. based on
2 coordinates of chart) or an instance of
Graphics3d for a 3D plot (i.e.
based on 3 coordinates of chart)